Predictive information in a nonequilibrium critical model

TL;DR

This paper introduces predictive information as a universal order parameter for phase transitions, especially in nonequilibrium systems, demonstrating its divergence at critical points through a stochastic model example.

Contribution

It proposes using predictive information to identify phase transitions in nonequilibrium systems, providing a new approach beyond traditional symmetry-based methods.

Findings

Predictive information diverges as log(T) at the transition point.

It remains constant away from the transition.

Demonstrated on a stochastic nonequilibrium model.

Abstract

We propose predictive information, that is information between a long past of duration T and the entire infinitely long future of a time series, as a universal order parameter to study phase transitions in physical systems. It can be used, in particular, to study nonequlibrium transitions and other exotic transitions, where a simpler order parameter cannot be identifies using traditional symmetry arguments. As an example, we calculate predictive information for a stochastic nonequilibrium dynamics problem that forms an absorbing state under a continuous change of a parameter. The information at the transition point diverges as log(T), and a smooth crossover to constant away from the transition is observed.